As I've grown older and been exposed to more and more people, I have noticed that people consider me a great resource for help. I feel good about this, but I don't know how to approach certain situations. A few months ago, I was contacted by a girl who was self-harming and didn't want anyone to know. Of course I told an adult, but are there ways that I can also contribute to the person's well being in these situations? I consider myself very outgoing, and I enjoy comforting people, but I need to ensure that I am doing things correctly if you will.

Well, it's risky, depending on the situation. Everyone is different, everyone reacts in so many ways.
The best thing you can do is to be there for them, next to them, show them that they're not alone. That usually helps. Help them escape the pressure by submerging it.
Laughter can help, if you're good at making people laugh you can help them escape such moods easier. Or you can tell them about a few hobbies, if they'd like to join in on them with you. Anything to keep them get away from the sadness.
Be there for them and then help them with escaping the compulsion.

Hey Eli, you sound like an amazing guy and friend. I think you can get sucked up into really heavy situations very quickly when you're a kind and loving person. I know my sister went through some difficult times, but at the end of the day she needed to do the most important things on her own and got help from people who were trained. You sound like you're doing exactly what you should - just being there is incredible to someone in need. You can't always have the answers so don't be afraid to reach out to others if you think something really bad might happen. Best wishes to your friend...

There was a guy at my school who I would always bump into at school, he was never in any of my classes, but I would say hey to him if I walked passed him. One time I did manage to have a little conversation with him. I noticed he had lots of cuts and scars on his upper arm.

In hindsight, I know I should have done something to help him as these were obvious self harm scars, but at the time I didn't want to say anything as I thought it wasn't any of my business.

You did the right thing. You probably saved that girls life. Don't be afraid to help others. If you see something isn't right, make a change and do something about it.